Geometric Decomposition of Eddy Feedbacks in Barotropic Systems

2015 ◽  
Vol 45 (4) ◽  
pp. 1009-1024 ◽  
Author(s):  
Stephanie Waterman ◽  
Jonathan M. Lilly
Keyword(s):  
Mean Flow ◽  
Flux Divergence ◽  
Atmospheric Flows ◽  
Anisotropic Part ◽  
Beta Plane ◽  
Flow Interactions ◽  
Geometric Decomposition ◽  
Vorticity Flux ◽  
Dynamical Quantity ◽  
Mean Circulation

AbstractIn oceanic and atmospheric flows, the eddy vorticity flux divergence—denoted “F” herein—emerges as a key dynamical quantity, capturing the average effect of fluctuations on the time-mean circulation. For a barotropic system, F is derived from the horizontal velocity covariance matrix, which itself can be represented geometrically in terms of the so-called variance ellipse. This study proves that F may be decomposed into two different components, with distinct geometric interpretations. The first arises from variations in variance ellipse orientation, and the second arises from variations in the kinetic energy of the anisotropic part of the velocity fluctuations, which can be seen as a function of variance ellipse size and shape. Application of the divergence theorem shows that F integrated over a closed region is explained entirely by separate variations in these two quantities around the region periphery. A further decomposition into four terms shows that only four specific spatial patterns of ellipse variability can give rise to a nonzero eddy vorticity flux divergence. The geometric decomposition offers a new tool for the study of eddy–mean flow interactions, as is illustrated with application to an unstable eastward jet on a beta plane.

scholarly journals A New Method to Estimate Three-Dimensional Residual-Mean Circulation in the Middle Atmosphere and Its Application to Gravity Wave–Resolving General Circulation Model Data

2013 ◽  
Vol 70 (12) ◽  
pp. 3756-3779 ◽  
Author(s):  
Kaoru Sato ◽  
Takenari Kinoshita ◽  
Kota Okamoto
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
General Circulation ◽  
Three Dimensional ◽  
Circulation Model ◽  
Mean Flow ◽  
Flux Divergence ◽  
Mean Circulation ◽  
Residual Mean Circulation ◽  
Wave Induced

Abstract A new method is proposed to estimate three-dimensional (3D) material circulation driven by waves based on recently derived formulas by Kinoshita and Sato that are applicable to both Rossby waves and gravity waves. The residual-mean flow is divided into three, that is, balanced flow, unbalanced flow, and Stokes drift. The latter two are wave-induced components estimated from momentum flux divergence and heat flux divergence, respectively. The unbalanced mean flow is equivalent to the zonal-mean flow in the two-dimensional (2D) transformed Eulerian mean (TEM) system. Although these formulas were derived using the “time mean,” the underlying assumption is the separation of spatial or temporal scales between the mean and wave fields. Thus, the formulas can be used for both transient and stationary waves. Considering that the average is inherently needed to remove an oscillatory component of unaveraged quadratic functions, the 3D wave activity flux and wave-induced residual-mean flow are estimated by an extended Hilbert transform. In this case, the scale of mean flow corresponds to the whole scale of the wave packet. Using simulation data from a gravity wave–resolving general circulation model, the 3D structure of the residual-mean circulation in the stratosphere and mesosphere is examined for January and July. The zonal-mean field of the estimated 3D circulation is consistent with the 2D circulation in the TEM system. An important result is that the residual-mean circulation is not zonally uniform in both the stratosphere and mesosphere. This is likely caused by longitudinally dependent wave sources and propagation characteristics. The contribution of planetary waves and gravity waves to these residual-mean flows is discussed.

scholarly journals A Geometric Interpretation of Zonostrophic Instability

2020 ◽  
Vol 50 (9) ◽  
pp. 2759-2779
Author(s):  
Georgios Kontogiannis ◽  
Nikolaos A. Bakas
Keyword(s):  
Stress Tensor ◽  
Stability Boundary ◽  
Geometric Interpretation ◽  
Mean Flow ◽  
Ginzburg Landau ◽  
Zonal Jets ◽  
Beta Plane ◽  
Geometric Decomposition ◽  
Eddy Dynamics ◽  
The Stability

AbstractThe zonostrophic instability that leads to the emergence of zonal jets in barotropic beta-plane turbulence is analyzed through a geometric decomposition of the eddy stress tensor. The stress tensor is visualized by an eddy variance ellipse whose characteristics are related to eddy properties. The tilt of the ellipse principal axis is the tilt of the eddies with respect to the shear, and the eccentricity of the ellipse is related to the eddy anisotropy, and its size is related to the eddy kinetic energy. Changes of these characteristics are directly related to the vorticity fluxes forcing the mean flow. The statistical state dynamics of the turbulent flow closed at second order is employed as it provides an analytic expression for both the zonostrophic instability and the stress tensor. For the linear phase of the instability, the stress tensor is analytically calculated at the stability boundary. For the nonlinear equilibration of the instability the tensor is calculated in the limit of small supercriticality in which the amplitude of the jet velocity follows Ginzburg–Landau dynamics. It is found that, dependent on the characteristics of the forcing, the jet is accelerated either because the jet primarily anisotropizes the eddies so as to produce upgradient fluxes, or because the jet changes the eddy tilt. The instability equilibrates as these changes are partially reversed by the nonlinear jet–eddy dynamics.

scholarly journals Eddy-Mean Flow Interactions in the Along-Stream Development of a Western Boundary Current Jet: An Idealized Model Study

2011 ◽  
Vol 41 (4) ◽  
pp. 682-707 ◽  
Author(s):  
Stephanie Waterman ◽  
Steven R. Jayne
Keyword(s):  
Western Boundary Current ◽  
Upstream Region ◽  
Western Boundary ◽  
Driving Mechanism ◽  
Boundary Current ◽  
Mean Flow ◽  
Model Study ◽  
Recirculation Gyres ◽  
Flow Interactions ◽  
Mean Circulation

A theoretical study on the role of eddy-mean flow interactions in the time-mean dynamics of a zonally evolving, unstable, strongly inertial jet in a configuration and parameter regime that is relevant to oceanic western boundary current (WBC) jets is described. Progress is made by diagnosing the eddy effect on the time-mean circulation, examining the mechanism that permits the eddies to drive the time-mean recirculation gyres, and exploring the dependence of the eddy effect on system parameters. It is found that the nature of the eddy-mean flow interactions in this idealized configuration is critically dependent on along-stream position, in particular relative to the along-stream evolving stability properties of the time-mean jet. Just after separation from the western boundary, eddies act to stabilize the jet through downgradient fluxes of potential vorticity (PV). Downstream of where the time-mean jet has (through the effect of the eddies) been stabilized, eddies act to drive the time-mean recirculations through the mechanism of an upgradient PV flux. This upgradient flux is permitted by an eddy enstrophy convergence downstream of jet stabilization, which results from the generation of eddies in the upstream region where the jet is unstable, the advection of that eddy activity along stream by the jet, and the dissipation of the eddies in the region downstream of jet stabilization. It is in this region of eddy decay that eddies drive the time-mean recirculations through the mechanism of nonlinear eddy rectification, resulting from the radiation of waves from a localized region. It is found that similar mechanisms operate in both barotropic and baroclinic configurations, although differences in the background PV gradient on which the eddies act implies that the recirculation-driving mechanism is more effective in the baroclinic case. This study highlights the important roles that eddies play in the idealized WBC jet dynamics considered here of stabilizing the jet and driving the flanking recirculations. In the absence of eddy terms, the magnitude of the upper-ocean jet transport would be significantly less and the abyssal ocean recirculations (and their significant enhancement to the jet transport) would be missing altogether.

scholarly journals Wave-mean flow interactions in the upper atmosphere

1973 ◽  
Vol 4 (1-4) ◽  
pp. 327-343 ◽  
Author(s):  
Richard S. Lindzen
Keyword(s):  
Upper Atmosphere ◽  
Mean Flow ◽  
Flow Interactions

scholarly journals The influence of idealized surface heterogeneity on virtual turbulent flux measurements

2018 ◽  
Vol 18 (7) ◽  
pp. 5059-5074 ◽  
Author(s):  
Frederik De Roo ◽  
Matthias Mauder
Keyword(s):  
Energy Budget ◽  
Turbulent Flux ◽  
Surface Heterogeneity ◽  
Surface Fluxes ◽  
Convective Conditions ◽  
Mean Flow ◽  
Flux Divergence ◽  
Length Scales ◽  
Flux Measurements ◽  
The Mean

Abstract. The imbalance of the surface energy budget in eddy-covariance measurements is still an unsolved problem. A possible cause is the presence of land surface heterogeneity, which affects the boundary-layer turbulence. To investigate the impact of surface variables on the partitioning of the energy budget of flux measurements in the surface layer under convective conditions, we set up a systematic parameter study by means of large-eddy simulation. For the study we use a virtual control volume approach, which allows the determination of advection by the mean flow, flux-divergence and storage terms of the energy budget at the virtual measurement site, in addition to the standard turbulent flux. We focus on the heterogeneity of the surface fluxes and keep the topography flat. The surface fluxes vary locally in intensity and these patches have different length scales. Intensity and length scales can vary for the two horizontal dimensions but follow an idealized chessboard pattern. Our main focus lies on surface heterogeneity of the kilometer scale, and one order of magnitude smaller. For these two length scales, we investigate the average response of the fluxes at a number of virtual towers, when varying the heterogeneity length within the length scale and when varying the contrast between the different patches. For each simulation, virtual measurement towers were positioned at functionally different positions (e.g., downdraft region, updraft region, at border between domains, etc.). As the storage term is always small, the non-closure is given by the sum of the advection by the mean flow and the flux-divergence. Remarkably, the missing flux can be described by either the advection by the mean flow or the flux-divergence separately, because the latter two have a high correlation with each other. For kilometer scale heterogeneity, we notice a clear dependence of the updrafts and downdrafts on the surface heterogeneity and likewise we also see a dependence of the energy partitioning on the tower location. For the hectometer scale, we do not notice such a clear dependence. Finally, we seek correlators for the energy balance ratio in the simulations. The correlation with the friction velocity is less pronounced than previously found, but this is likely due to our concentration on effectively strongly to freely convective conditions.

Advancing the simulation of mesoscale eddies: Backscatter schemes in eddy-permitting ocean simulations

2021 ◽  
Author(s):  
Stephan Juricke ◽  
Sergey Danilov ◽  
Marcel Oliver ◽  
Nikolay Koldunov ◽  
Dmitry Sidorenko ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Large Scale ◽  
Mesoscale Eddy ◽  
Ocean Model ◽  
Mean Flow ◽  
Ocean Coupling ◽  
Climate Simulations ◽  
Flow Interactions ◽  
To Come ◽  
Eddy Dynamics

<p>Capturing mesoscale eddy dynamics is crucial for accurate simulations of the large-scale ocean currents as well as oceanic and climate variability. Eddy-mean flow interactions affect the position, strength and variations of mean currents and eddies are important drivers of oceanic heat transport and atmosphere-ocean-coupling. However, simulations at eddy-permitting resolutions are substantially underestimating eddy variability and eddy kinetic energy many times over. Such eddy-permitting simulations will be in use for years to come, both in coupled and uncoupled climate simulations. We present a set of kinetic energy backscatter schemes with different complexity as alternative momentum closures that can alleviate some eddy related biases such as biases in the mean currents, in sea surface height variability and in temperature and salinity. The complexity of the schemes reflects in their computational costs, the related simulation improvements and their adaptability to different resolutions. However, all schemes outperform classical viscous closures and are computationally less expensive than a related necessary resolution increase to achieve similar results. While the backscatter schemes are implemented in the ocean model FESOM2, the concepts can be adjusted to any ocean model including NEMO.</p>

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